The announcement triggered a spat with a Melbourne City councillor who said the decision was "appalling", and prompted an avalanche of criticism on Premier Daniel Andrews' Facebook page.

Hundreds of people condemned the decision in a torrent of negative comments and Facebook posts, with many urging the government to reconsider the move.

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How Federation Square might look from the air.

Age readers have described the plan as "absolutely disgraceful", a "monstrous carbuncle" and an "appalling use of public space".

Former premier Ted Baillieu was also drawn into the fray, criticising the plan in a radio interview.

Wednesday's announcement follows more than a year of speculation about the deal. Construction is set to start in 2019 and finish the following year.

However, the government insists that Apple will foot the cost of the demolition and construction, which will also include the creation of 500 square metres of new public space.

How the new Apple store will look at Federation Square

The Koorie Heritage Trust, which is based in the Yarra building, will be moved to a new site within Federation Square.

Tourism Minister John Eren insisted the government offered no funding or other incentives to entice Apple to undertake the project.

An artist's impression of the view from the new Apple store.

The company will lease the building but the terms of that arrangement were not made public.

Mr Eren said the Yarra building needed commercial tenants to ensure the entire precinct was viable.

How the new Apple store will look at Federation Square

"It does need to generate some money through commercial ventures," he said.

Mr Eren confirmed negotiations had been underway for about two years.

Apple retail senior vice-president Angela Ahrendts said the company was thrilled to move forward with the plans and was honoured to "call the world-class galleries and museums of Melbourne our neighbours".

There are large Apple stores in suburban shopping centres across Melbourne as well as a shop selling Apple products directly opposite Federation Square.

The government insisted the redevelopment would create 200 jobs.

But Melbourne City councillor Rohan Leppert slammed the plans, accusing the government of failing to consult the public or councillors.

"It has radically different architecture and converts cultural space to commercial space – but [planning minister] Richard Wynne has made that change to the planning scheme by exempting himself from the normal public participation requirements," Cr Leppert, a Greens member, told The Age.

"The bottom line is that this is Melbourne's civic square and Melburnians deserved to have their say."

In response, a government spokesman said advice had been sought from Victorian government architect Jill Garner and Federation Square's original architect Donald Bates.

"Mr Bates said the location was suitable for a commercial development and designed as such, and commercial and retail uses has always been part of its vision," he said.

The architect himself said the Yarra building had not been particularly successful in its "various iterations".

"I don't have a huge problem with it being replaced with something that would be more viable," Mr Bates said.

He also said it was appropriate that the new construction look substantially different from the Yarra building rather than mimicking the current "aesthetic".

Ex-premier Ted Ballieu, who is also an architect, described the plan as a "bananas idea". He told radio station 3AW said it was "completely incongruous" with the square's existing buildings.

"It could only be a financial solution to a financial problem," he said.

Mr Baillieu said he did not have a problem with commercial activity in public places, including restaurants and cafes. But handing part of Federation Square over to Apple was going "way too far".

Federation Square and Apple were both powerful "brands" but only one could survive in the proposed arrangement, Mr Ballieu said.

"I don't think Fed Square is going to have an easy time with Apple on top of it."

Mr Baillieu said the deal would allow Apple to, in effect, "own the square in terms of the way the space is used".

The Koorie Heritage Trust moved into the Yarra Building just two years ago.

But its chief executive Tom Mosby said it was already outgrowing its current space and had been assured there would be a new, larger site within Federation Square.

"In terms of our location it's been fantastic. We've certainly more than doubled visitation," he said.

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"[But we're] starting to feel the constraints of the space."

Federation Square chief executive Jonathan Tribe said the new building would take up less space than the Yarra building.